Risk-adjusted performance: Sharpe, alpha, beta and tracking error

Worked example: the two 8% funds

Both funds returned 8%. Risk-free rate is 4%.

• Fund A: volatility (standard deviation) of 10%
• Fund B: volatility of 16%

Same return, but Fund A's Sharpe of 0.40 crushes Fund B's 0.25. Fund A generated 60% more return per unit of risk. That is the number that wins the mandate.

How to read it: higher is better. As a rough industry heuristic (not a guarantee), a Sharpe above 1.0 is considered strong for a diversified strategy, and long-run broad equity indices often land somewhere below 1.0 over full cycles. Do not fixate on the exact threshold; use it to compare funds *in the same category over the same period*.

The CFA Institute's overview of the Sharpe ratio is a solid free reference for the underlying theory.

Beta: how much market you are riding

Beta measures sensitivity to the overall market.

• Beta = 1.0: the fund moves in line with its benchmark.
• Beta = 1.3: expect it to rise (and fall) about 30% more than the market.
• Beta = 0.7: it dampens market moves, falling less in selloffs.

Beta is not skill. A manager can manufacture high returns in a bull market simply by running a beta of 1.5. That is leverage on the market, not talent. This is exactly why allocators separate beta (cheap, buy it through an index fund) from alpha (rare, worth paying for).

Alpha: the part the manager actually earned

Alpha is the return above what beta alone would predict. It is the manager's value-add after stripping out the market ride.

Simplified version:

Worked example

• Fund return (Rp): 8%
• Risk-free (Rf): 4%
• Benchmark return (Rm): 6%
• Beta: 1.2

The fund delivered 1.6% of genuine outperformance beyond what its market exposure "should" have produced. Positive alpha is the holy grail. Most active managers struggle to produce it consistently after fees, which is a big reason index funds have taken enormous market sharemarket shareThe percentage of total industry sales your company captures in a given period. It measures competitive position relative to rivals in a defined market.Voir la définition complète → (US passive equity assets crossed roughly half of the equity fund market in the early 2020s per widely cited industry data; treat the exact split as an estimate).

Tracking error: how far you stray from the benchmark

Tracking error is the standard deviation of the *difference* between a fund's returns and its benchmark's returns. It measures how tightly a manager hugs their index.

• Low tracking error (say 1% to 2%): the fund stays close to its benchmark. Typical of "enhanced index" or closet-benchmark strategies.
• High tracking error (6%+): the manager takes big, differentiated bets. Typical of high-conviction active funds.

Neither is inherently good or bad. It depends on the mandate. A pension hiring a "core US large-cap" manager wants *low* tracking error and steady, modest alpha. A family office hiring a concentrated stock-picker *wants* high tracking error, because they are paying for bold, differentiated bets.

The mistake allocators punish: high fees with low tracking error. If you charge active fees but hug the index, the client is paying a premium for beta they could buy for a few basis points. Regulators noticed too. Europe's markets authority ESMA (European Securities and Markets Authority) has scrutinised "closet indexing" (funds marketed as active but effectively tracking their benchmark) for exactly this reason.

Information ratio: alpha per unit of active risk

The information ratio (IR) is the Sharpe ratio's sibling for active managers. It measures active return per unit of tracking error.

Formula:

Worked example: back to our two funds

Both funds returned 8%. Benchmark returned 6%, so both have 2% of active return.

• Fund A: tracking error of 4%
• Fund B: tracking error of 8%

Fund A produced the same 2% of outperformance while straying half as far from the benchmark. Its IR of 0.50 signals a more efficient, more repeatable process. An IR around 0.5 is often described as good and 1.0 as excellent (industry rule of thumb, not a law).

This is the punchline of the hook: identical returns, but Fund A wins on both Sharpe and information ratio because it took less risk to get there. Lower volatility, tighter tracking error, same reward. That is what an investment committee funds.

Putting it together: reading a real factsheet

When a fund factsheet lands on your desk, scan these five lines in order:

1. Return vs benchmark. Did they beat it? By how much (that is your active return)?

2. Beta. Is the outperformance just extra market exposure? A beta well above 1.0 explains a lot of "outperformance" in a rising market.

3. Alpha. Positive and persistent across multiple periods? One good year is noise.

4. Sharpe ratio. Compare it only against peers in the same category and same time window.

5. Tracking error and information ratio. Does the risk-taking match the mandate, and is the alpha efficient?

The comparison trap to avoid

Never compare Sharpe ratios across different asset classes or different time periods. A bond fund's Sharpe and an emerging-market equity fund's Sharpe are not measured on the same volatility scale, and a Sharpe from a calm year flatters everyone. Always compare like with like, over the same window.

A note on fees

Every one of these metrics should be computed *net of fees*. A gross alpha of 2% is meaningless if the fund charges 1.9%. In both the US and Europe, cost disclosure is regulated: US mutual funds report expense ratios under SEC rules, and European retail funds disclose costs via the PRIIPs KID (Packaged Retail and Insurance-based Investment Products Key Information Document). Always find the net number.

Key Takeaways

• Same return is not the same performance. Divide reward by risk: the fund with lower volatility (higher Sharpe) or tighter tracking error (higher information ratio) is the more fundable one.
• Separate beta from alpha. Beta is cheap market exposure you can buy in an index fund. Alpha is genuine, rare, manager-generated return. Do not pay active fees for disguised beta.
• Match tracking error to the mandate. Low tracking error suits a core allocation, high tracking error suits a high-conviction bet. The sin is high fees with low tracking error (closet indexing), which ESMA and others actively scrutinise.
• Always compare like with like, net of fees. Same asset class, same time window, after all costs. A Sharpe ratio out of context is worthless.
• Memorise two formulas: Sharpe = (Rp − Rf) / volatility, and Information Ratio = (Rp − Rb) / tracking error. They answer the two questions every allocator asks: return per unit of total risk, and alpha per unit of active risk.